I have problems with understanding stationary wave vibration

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Tinamuline

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stationary wave

Can someone tell me why the particles in the same loop of a stationary (or standing) wave vibrate with the same phase?
Back to basic, stationary wave is formed by the superposition of incident and reflected wave. Can I say it is formed by superposition of 2 progressive waves under a specific condition? If it is true, why nodes (zero displacement) remain nodes, whereas antinodes can varies their displacement from maximum to zero.

Thank you for your help.
 

Re: I have problems with understanding stationary wave vibra

When you have two waves propagating in opposite directions, given by:
f1=a*sin(w*t-k*x) and f2=a*sin(w*t+k*x) and you add them, you will get:
f=2*a*cos(k*x)*sin(w*t).
The last equation answers your question.
 

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